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Journal of the Optical Society of America B

Journal of the Optical Society of America B


  • Vol. 22, Iss. 2 — Feb. 1, 2005
  • pp: 315–322

Triplet–triplet annihilation in viscous solutions as an example of non-Fickian diffusion

Pawel Borowicz and Bernhard Nickel  »View Author Affiliations

JOSA B, Vol. 22, Issue 2, pp. 315-322 (2005)

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Diffusion-controlled triplet–triplet annihilation is analyzed in terms of non-Fickian diffusion. The description is based on the second Fick’s law with a time-dependent diffusion coefficient. We introduce the time-dependent diffusion coefficient because of the interaction of two associated relaxation phenomena: first-order decay and diffusion-controlled annihilation. The equation for the time-dependent rate parameter k2A(t) obtained from the model proposed is compared with the standard Smoluchowski expression. The new equation is applied for the evaluation of the kinetic data of the diffusion-controlled triplet–triplet annihilation of anthracene. The limits of the applicability of the proposed model are discussed.

© 2005 Optical Society of America

OCIS Codes
(260.0260) Physical optics : Physical optics
(260.2160) Physical optics : Energy transfer
(300.0300) Spectroscopy : Spectroscopy
(300.6390) Spectroscopy : Spectroscopy, molecular
(300.6500) Spectroscopy : Spectroscopy, time-resolved
(300.6550) Spectroscopy : Spectroscopy, visible

Pawel Borowicz and Bernhard Nickel, "Triplet-triplet annihilation in viscous solutions as an example of non-Fickian diffusion," J. Opt. Soc. Am. B 22, 315-322 (2005)

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  1. T. Alfrey, Jr., E. F. Gurnee, and W. G. Lloyd, "Diffusion in glassy polymers," J. Polym. Sci., Part C: Polym. Lett. 12, 249-261 (1966). [CrossRef]
  2. J. Crank, The Mathematics of Diffusion , 2nd ed. (Clarendon, Oxford, UK, 1979), pp. 254-257.
  3. P. F. Nealey, R. E. Cohen, and A. S. Argon, "Limited-supply non-Fickian diffusion in glassy polymers," Polymer 36, 3687-3695 (1995). [CrossRef]
  4. M. Sanopoulou and D. F. Stamatialis, "Study of the transition from Fickian to Case II sorption kinetics in the system poly(ethyl methacrylate) - liquid methyl alcohol," Polymer 42, 1429-1439 (2001). [CrossRef]
  5. R. Kimmich, "Strange kinetics, porous media and NMR," Chem. Phys. 284, 253-285 (2002). [CrossRef]
  6. C. Chen, B. Han, J. Li, T. Shang, J. Zou, and W. Jiang, "A new model on the diffusion of small molecule penetrants in dense polymer membranes," J. Membr. Sci. 187, 109-118 (2001). [CrossRef]
  7. L. Massaro and X. X. Zhu, "Physical model of diffusion for polymer solutions, gels and solids," Prog. Polym. Sci. 24, 731-775 (1999). [CrossRef]
  8. S. J. Huang, C. J. Durning, and B. D. Freeman, "Modeling weakly non-linear two-stage sorption kinetics in glassy polymer films," J. Membr. Sci. 143, 1-11 (1998). [CrossRef]
  9. R. Ash and S. E. Espenhahn, "Transport through a slab membrane governed by a concentration-dependent diffusion coefficient. Part I. The four time-lags: some general considerations," J. Membr. Sci. 154, 105-119 (1999). [CrossRef]
  10. M. S. Vicente and J. C. Y. Gottifredi, "Effect of volume changes due to absorption in polymer membranes," J. Membr. Sci. 169, 249-254 (2000). [CrossRef]
  11. M. A. Zahran, E. M. Abulwafa, and S. A. Elwakil, "The fractional Fokker-Planck equation on comb-like model," Physica A 323, 237-248 (2003). [CrossRef]
  12. S. Zhou, Z. Weng, Z. Huang, and Z. Pan, "Sorption kinetics of 1-fluoro-1,1-dichloroethane in vinylidene chloride-acrylonitrile-styrene terpolymer," Eur. Polym. J. 38, 211-217 (2002). [CrossRef]
  13. P. Castiglione, A. Mazzino, P. Muratore-Ginanneschi, and A. Vulpiani, "On strong anomalous diffusion," Physica D 134, 75-93 (1999). [CrossRef]
  14. S. Zou, J. Xia, and A. D. Koussis, "Analytical solutions to non-Fickian subsurface in uniform groundwater flow," J. Hydrol. 179, 237-258 (1996). [CrossRef]
  15. T. Ishii, "Theoretical investigation of anomalous diffusion in a random lattice," Solid State Commun. 116, 327-331 (2000). [CrossRef]
  16. C. A. Parker, "Triplet state processes in fluid solutions," Ber. Bunsenges. Phys. Chem. 73, 764-772 (1969).
  17. B. Nickel, H. E. Wilhelm, and C. P. Jänsch, "Effect of the Förster energy transfers S1 + S1 --> S0 + Sn and S1 + T1 --> S0 + Tm on the time dependence of the delayed fluorescence from aromatic compounds: anti-Smoluchowski and Smoluchowski temporal behaviour," Opt. Spectrosc. 83, 541-556 (1997).
  18. M. von Smoluchowski, "Versuch einer mathematischen theorie der koagulationskinetik kolloider Lösungen," Z. Phys. Chem. (Frankfurt am Main) 92, 129-168 (1917).
  19. A. V. Barzykin, K. Seki, and M. Tachiya, "Kinetics of diffusion-assisted reactions in microheterogeneous systems," Adv. Colloid Interface Sci. 89-90, 47-140 (2001). [CrossRef] [PubMed]
  20. A. H. Alwattar, M. D. Lumb, and J. B. Birks, "Diffusion-controlled rate processes," in Organic Molecular Photophysics , J. B. Birks, ed. (Wiley-Interscience, London, 1973), Vol. 1, p. 417.
  21. F. C. Collins and G. E. Kimball, "Diffusion-controlled reaction rates," J. Colloid Sci. 4, 425-437 (1949). [CrossRef]
  22. H. Wilhelm, "Anti-Smoluchowski-Zeitverlauf der verzögerten fluoreszenz aromatischer verbindungen," Ph.D. thesis (Cuvillier Verlag, Göttingen, Germany, 1995), p. 6.
  23. C. Jänsch, "Anwendung von Smoluchowskis Theorie auf die Kinetik der diffusionskontrollierten Triplett-Triplett-Annihilation aromatischer Verbindungen," Ph.D. thesis (Cuvillier Verlag, Göttingen, Germany, 1997), p. 2.
  24. J. Saltiel and B. W. Atwater, "Spin-statistical factors in diffusion-controlled reactions," Adv. Photochem. 14, 1-90 (1988).
  25. B. Dick and B. Nickel, "Accessibility of the lowest quintet state of organic molecules through triplet-triplet annihilation; an INDO CI study," Chem. Phys. 78, 1-16 (1983). [CrossRef]
  26. B. Nickel, H. E. Wilhelm, and A. A. Ruth, "Anti-Smoluchowski time dependence of the delayed fluorescence from anthracene in viscous solutions due to triplet-triplet annihilation. Effect of Förster energy transfer S1 + T1 --> S0 + Tn on the initial spatial distribution of molecules in T1," Chem. Phys. 188, 267-287 (1994). [CrossRef]
  27. R. M. Noyes, "Effects of diffusion rates on chemical kinetics," Prog. React. Kinet. 1, 129-160 (1961).
  28. D. L. Dexter, "A theory of sensitized luminescence in solids," J. Phys. Chem. 21, 836-850 (1953). [CrossRef]
  29. G. Wilemski and M. Fixman, "General theory of diffusion-controlled reactions," J. Chem. Phys. 58, 4009-4019 (1973). [CrossRef]
  30. P. R. Butler and M. J. Pilling, "Long range mechanism for the temperature dependence of the ratio of delayed monomer and delayed excimer fluorescence following triplet-triplet annihilation in liquids," J. Chem. Soc., Faraday Trans. 2 73, 886-894 (1977). [CrossRef]
  31. J. P. Pilling and S. A. Rice, "Theoretical model for diffusion controlled reactions of solvated electrons, incorporating a tunnelling mechanism," J. Chem. Soc., Faraday Trans. 2 71, 1563-1571 (1975). [CrossRef]
  32. J. P. Pilling and S. A. Rice, "Long range energy transfer by dipole-dipole and exchange interactions in rigid media and in liquids," J. Chem. Soc., Faraday Trans. 2 72, 792-801 (1976). [CrossRef]
  33. S. A. Adelman, "Focker-Planck equations for simple non-Markovian systems," J. Chem. Phys. 64, 124-130 (1976). [CrossRef]
  34. W. Dong, F. Baros, and J. C. André, "Non-Markovian effect on diffusion-controlled reactions," Ber. Bunsenges. Phys. Chem. 94, 269-274 (1990). [CrossRef]
  35. W. Dong and J. C. André, "Diffusion-controlled reactions.II. An approach based on generalized diffusion equation," J. Chem. Phys. 101, 299-306 (1994). [CrossRef]
  36. W. Dong, F. Baros, and J. C. André, "Diffusion-controlled reactions. I. Molecular dynamics simulation of a noncontinuum model," J. Chem. Phys. 91, 4643-4650 (1989). [CrossRef]
  37. J. Jasny, B. Nickel, and P. Borowicz, "Wavelength- and temperature-dependent measurement of the refractive indices," J. Opt. Soc. Am. B 21, 729-738 (2004). [CrossRef]
  38. E. G. Meyer and B. Nickel, "Diffusion coefficients of aromatic hydrocarbons in their lowest triplet state: anthracene in hexane, octane, hexadecane, perfluorohexane, and methylcyclohexane; pyrene and 9,10-diphenylanthracene in hexane," Z. Naturforsch. Teil A 35, 503-520 (1980).
  39. A. A. Ruth, B. Nickel, and H. Lesche, "Temperature dependence of viscosity and density of glass-forming alkenes," Z. Phys. Chem. (Munich) 175, 91-108 (1992). [CrossRef]
  40. P. R. Butler and M. J. Pilling, "Long range quenching of triplet phenantrene by copper ions in the liquid phase," Chem. Phys. 39, 33-36 (1979). [CrossRef]
  41. P. R. Butler and M. J. Pilling, "The breakdown of Förster kinetics in low viscosity liquids. An approximate analytical form for the time-dependent rate constant," Chem. Phys. 41, 239-243 (1979). [CrossRef]
  42. V. C. Sinclair, J. Monteath Robertson, and A. McL. Mathieson, "The crystal and molecular structure of anthracene. II. Structure investigation by the triple Fourier series method," Acta Crystallogr. 3, 251-256 (1950). [CrossRef]
  43. A. Bondi, "Van der Waals volumes and radii," J. Phys. Chem. 68, 441-451 (1964). [CrossRef]
  44. W. Liptay, J. Becker, D. Wehning, W. Lang, and Z. O. Burkhard, "The determination of molecular quantities from measurements on macroscopic systems II. The determination of electric dipole moments," Z. Naturforsch. Teil A 37, 1396-1408 (1982).
  45. K. Rotkiewicz and Z. R. Grabowski, "Excited states of aminoanthracenes: an experimental approach to electron density distribution," Trans. Faraday Soc. 65, 3263-3278 (1969). [CrossRef]
  46. J. T. Edward, "Molecular volumes and the Stokes-Einstein equation," J. Chem. Educ. 47, 261-270 (1970). [CrossRef]
  47. M. Litniewski and J. Górecki, "On the applicability of the step function nonradiative lifetime model for diffusion controlled reactions," J. Chem. Phys. 119, 8464-8472 (2003). [CrossRef]
  48. M. Litniewski and J. Górecki, "Molecular dynamics tests of the Smoluchowski-Collins-Kimball model for fluorescence quenching of spherical molecules," Phys. Chem. Chem. Phys. 6, 72-83 (2004). [CrossRef]

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